Pease help with two circle questions

Question

I have to sent these questions solved at my teacher till 12:00 PM and i cant solve them please help me.. here are the questions

http://i46.tinypic.com/25zqcjt.jpg http://i49.tinypic.com/mj7jgx.jpg

if you can solve them and then take a pic of the solutions it would be a huge favor. Thanks

Answer 1

Here’s a large hint for one of them.

(22) Let $r=|OE|$ be the radius of the smaller circle and $R=|OC|$ the radius of the larger circle. Let $d$ be the distance from $O$ to the line $\overline{AB}$. Then by the Pythagorean theorem you have

$$\begin{align*} &r^2+36=R^2,\\ &d^2+20=r^2,\text{ and}\\ &d^2+y^2=R^2\;, \end{align*}$$

where $y=\frac12|AB|$. It’s possible to solve these equations for $y$ and hence for $|AB|$.